International
Tables for
Crystallography
Volume A
Space-group symmetry
Edited by M. I. Aroyo

International Tables for Crystallography (2016). Vol. A, ch. 3.5, pp. 826-851
https://doi.org/10.1107/97809553602060000933

Chapter 3.5. Normalizers of space groups and their use in crystallography

E. Koch,a* W. Fischera and U. Müllerb

aInstitut für Mineralogie, Petrologie und Kristallographie, Philipps-Universität, D-35032 Marburg, Germany, and bFachbereich Chemie, Philipps-Universität, D-35032 Marburg, Germany
Correspondence e-mail:  kochelke@mailer.uni-marburg.de

Footnotes

1 Sohncke (1879[link]) was the first to derive the 65 space-group types having only symmetry operations of the first kind (translations, rotations and screw rotations). As proposed by Flack (2003[link]), these are called the 65 Sohncke space-group types.

2 In previous editions, the symbols [Z^{1}], [Z^{2}] and [Z^{3}] [(z^{1}, z^{2})] were used.

3 For the use of the terms `point configuration' and `crystallographic orbit' and a comparison of them, see Koch & Fischer (1985[link]) and Sections 3.4.1[link] and 3.4.2[link] .